Honestly? The first I ever experienced of cosplay was people dressing up as characters from Harry Potter and Lord of the Rings so even before I decided to try it myself, I've never seen it as something that's exclusive to any particular media. The more the merrier, I say.

The more annoying thing for me is when conventions have a rule for their main masquerade contest being restricted to just anime, manga, and Japanese video game characters, leaving only the hall cosplay for all of the other outfits, even if the best outfit at the entire convention is not of Japanese origin. :^\

Definitely not a problem with me. I know people that have problems with me because I am working on Homestuck cosplays; and Homestuck, not being a manga or anime or anything from Japan, is hated by some of my friends. So I'm out of the loop a bit.
I know the term was coined from Japan, but there's so much more to cosplaying than just anime and manga and video games! I have seen really awesome cartoon cosplays and movie cosplays and I don't think that cosplaying something that isn't of Japanese origin shouldn't stop people from doing what they want to do.

I like seeing all kinds of cosplays done personally. Though I can see why soem fans might be getting a bit miffed if they see Batman at their Anime Con. Though for them to get really uptight about it eh.. not so much.

To be honest, most things I cosplay are of non-Japanese origin. I think it's annoying when people get annoyed at non-Japanese cosplays. :/
I mean, really, now. At the last con I went to, the absolute best cosplays there were Disney characters, Tim Burton characters, Homestuck characters, Doctor Who, etc.
Cosplay is universal; if you want to cosplay someone from an anime, go for it. From a Disney movie, go for it. But putting others down or not acknowledging them just because they're not cosplaying someone from Japan is ridiculous.

I've never met anybody who had an actual problem with it. The only people I've ever heard complain about it do so online, and they're almost always quite young and new to the hobby or poorly-adjusted and overly judgemental on other subjects too.

Thinking that all costumes must be from Japanese media is just such a silly idea that I ignore it entirely.

That's weird as it's often said cosplay started with Star Trek. I'm not sure if that's accurate though.

If you're talking about these cosplays at anime conventions, well if it bothers you look the other way. It's still odd as a lot of anime cons these days are holding panels for non-anime/video game subjects.

I have no problems with it; cosplay is cosplay no matter what the source the character is from. If someone enjoys it then who am I to say otherwise?
I find it kinda refreshing actually to see a Legolas or Superman wandering around in the sea of anime characters.